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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 1206-1216 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical experiments have been performed to study the geometric collision rate of heavy particles with finite inertia. The turbulent flow was generated by direct numerical integration of the full Navier-Stokes equations. The collision kernel peaked at a particle response time between the Kolmogorov and the large-eddy turnover times, implying that both the large-scale and small-scale fluid motions contribute, although in very different manners, to the collision rate. Both numerical results for frozen turbulent fields and a stochastic theory show that the collision kernel approaches the kinetic theory of Abrahamson [Chem. Eng. Sci. 30, 1371 (1975)] only at very large τp/Te, where τp is the particle response time and Te is the flow integral time scale. Our results agree with those of Sundaram and Collins [J. Fluid Mech. 335, 75 (1997)] for an evolving flow. A rapid increase of the collision kernel with the particle response time was observed for small τp/τk, where τk is the flow Kolmogorov time scale. A small inertia of τp/τk=0.5 can lead to an order of magnitude increase in the collision kernel relative to the zero-inertia particles. A scaling law for the collision kernel at small τp/τk was proposed and confirmed numerically by varying the particle size, inertial response time, and flow Reynolds number. A leading-order theory for small τp/τk was developed, showing that the enhanced collision is mainly a result of the nonuniform particle concentration that results from the interaction of heavy particles with local flow microstructures. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 2647-2651 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A fundamental tenet of statistical mechanics is that the rate of collision of two objects is related to the expectation value of their relative velocities. In pioneering work by Saffman and Turner [J. Fluid Mech. 1, 16 (1956)], two different formulations of this tenet are used to calculate the collision kernel Γ between two arbitrary particle size groups in a turbulent flow. The first or spherical formulation is based on the radial component wr of the relative velocity w between two particles: Γsph=2πR2〈|wr|〉, where wr=w⋅R/R, R is the separation vector, and R=|R|. The second or cylindrical formulation is based on the vector velocity itself: Γcyl=2πR2〈|w|〉, which is supported by molecular collision statistical mechanics. Saffman and Turner obtained different results from the two formulations and attributed the difference to the form of the probability function of w used in their work. A more careful examination reveals that there is a fundamental difference between the two formulations. An underlying assumption in the second formulation is that the relative velocity at any instant is locally uniform over a spatial scale on the order of the collision radius R, which is certainly not the case in turbulent flow. Therefore, the second formulation is not expected to be rigorously correct. In fact, both our analysis and numerical simulations show that the second formulation leads to a collision kernel about 25% larger than the first formulation in isotropic turbulence. For a simple uniform shear flow, the second formulation is about 20% too large. The two formulations, however, are equivalent for treating the collision rates among random molecules and the gravitational collision rates. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 10 (1998), S. 266-276 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical experiments have been performed to study the geometric collision rate of finite-size particles with zero inertia (i.e., fluid elements) in isotropic turbulence. The turbulent flow was generated by the pseudospectral method. We argue that the formulation of Saffman and Turner [J. Fluid Mech. 1, 16 (1956)] for the average collision kernel is correct only under the assumptions that the particles are kept in the system after collision and allowed to overlap in space. This was confirmed, for the first time, by numerical experiments to within a numerical uncertainty as small as 1%. Finite corrections to the Saffman and Turner result must be made if one applies the theory to actual coagulation process where particles are not allowed to overlap before collision and particles are removed from a given size group after collision. This is due to the fact that Saffman and Turner assumed a uniform, time-independent concentration field in their formulation of the average collision kernel, while in the actual modeling of population evolution the particle number concentration changes in time and may be locally nonuniform as a result of a biased removal process due to spatially nonuniform coagulation rates. However, the quantitative level of the deviations from the Saffman and Turner result remain to be explained. Numerical experiments in simple shear flow were also conducted to elaborate our findings. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 99 (1995), S. 9646-9659 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Analytical chemistry 66 (1994), S. 3681-3687 
    ISSN: 1520-6882
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Previous models of the renal concentrating mechanism employ ideal approximations of solution thermodynamics for membrane transport calculation. In three-dimensional models of the renal medulla, predicted urine concentrations reach levels where there idealized approximations begin to break down. In this paper we derive equations that govern membrane transport for non-dilute solutions and use these equations in a three-dimensional model of the concentrating mechanism. New numerical methods were employed that are more stable than those employed previously. Compared to ideal solution models, the urea non-ideality tends to increase predicted osmolarities, whereas NaCl non-ideality decreases predictions.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1573-0662
    Keywords: DMS oxidation ; sulfur chemistry ; gas-to-particule conversion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract A box model was constructed to investigate connections between the particulate MSA to non-sea-salt sulfate ratio, R, and DMS chemistry in a clean marine boundary layer. The simulations demonstrated that R varies widely with particle size, which must be taken into account when interpreting field measurements or comparing them with each other. In addition to DMS gas-phase chemistry, R in the submicron size range was shown to be sensitive to the factors dictating sulfate production via cloud processing, to the removal of SO2 from the boundary layer by dry deposition and sea-salt oxidation, to the entrainment of SO2 from the free troposphere, to the relative concentration of sub- and supermicron particles, and to meteorology. Three potential explanations for the increase of R toward high-latitudes during the summer were found: larger MSA yields from DMS oxidation at high latitudes, larger DMSO yields from DMS oxidation followed by the conversion of DMSO to MSA at high latitudes, or lower ambient H2O2 concentrations at high latitudes leading to less efficient sulfate production in clouds. Possible reasons for the large seasonal amplitude of R at mid and high latitudes include seasonal changes in the partitioning of DMS oxidation to the OH and NO3 initiated pathways, seasonal changes in the concentration of species participating the DMS-OH reaction pathway, or the existence of a SO2 source other than DMS oxidation in the marine boundary layer. Even small anthropogenic perturbations were shown to have a potential to alter the MSA to non-sea-salt sulfate ratio.
    Type of Medium: Electronic Resource
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